A363051 a(n) = Sum_{b=0..floor(sqrt(n/2)), n-b^2 is square} b.

0, 1, 0, 0, 1, 0, 0, 2, 0, 1, 0, 0, 2, 0, 0, 0, 1, 3, 0, 2, 0, 0, 0, 0, 3, 1, 0, 0, 2, 0, 0, 4, 0, 3, 0, 0, 1, 0, 0, 2, 4, 0, 0, 0, 3, 0, 0, 0, 0, 6, 0, 4, 2, 0, 0, 0, 0, 3, 0, 0, 5, 0, 0, 0, 5, 0, 0, 2, 0, 0, 0, 6, 3, 5, 0, 0, 0, 0, 0, 4, 0, 1, 0

Offset: 1

Author

Darío Clavijo, May 14 2023

Keywords

• nonn

Comments

a(n) = 0 if n in A022544.

a(n) > 0 if n in A001481.

Links

• Project Euler, Problem 273: Sum of Squares

Crossrefs

Cf. A022544, A001481, A362961.

Programs

Maple

A363051 := proc(n)
    local x,a ;
    a := 0 ;
    for x from 1 do
        if x^2 > n/2 then
            return a;
        end if;
        if issqr(n-x^2) then
            a := a+x ;
        end if;
    end do:
end proc:
seq(A363051(n),n=1..100) ; # R. J. Mathar, Jan 31 2024

Mathematica

a[n_]:=Sum[b Boole[IntegerQ[Sqrt[n-b^2]]],{b,0,Floor[Sqrt[n/2]]}]; Array[a,83] (* Stefano Spezia, May 15 2023 *)

Python

from gmpy2 import *
a = lambda n: sum([b for b in range(0, isqrt(n >> 1) + 1) if is_square(n - (b*b))])
print([a(n) for n in range(1, 84)])

Python

from sympy.solvers.diophantine.diophantine import diop_DN
def A363051(n): return sum(min(a) for a in diop_DN(-1,n))>>1 # Chai Wah Wu, May 16 2023